A solution to Crouzeix's conjecture

Abstract

We provide a proof of Crouzeix's conjecture, which combines the tools developed previously for weaker estimates with a simple perturbation lemma for $2$-dilations. Applying the lemma to the iterates $f^n$ in the double-layer potential representation yields the conjectured bound.

7 pages, streamlined presentation and added further remarks and references as well as more detailed AI declaration